Karole Armitage/Armitage Gone! Dance (Friday, Saturday, Tuesday and Thursday; through Feb. 9) Karole Armitage has borne the heavy mantle of innovation since her 1981 “Drastic-Classicism,” a vision of punk ballerinas in feet-behind-head extensions set to earsplitting guitar. The premiere of that work was at the then-named Dance Theater Workshop, now New York Live Arts, where Ms. Armitage’s company will present her new work, “Mechanics of the Dance Machine,” set to music by Gabriel Prokofiev (grandson of the more famous Serge). In this piece the choreographer invites the audience onstage to participate in the performance by following light cues, allowing them to see the dancers up close. In a nontheater environment, you’d just call it an installation. But therein lies the challenge for Ms. Armitage: constructing a coherent theatrical experience from this particular way of presenting a work. An added draw: The former New York City Ballet principal dancer Charles Askegard has joined the cast. At 7:30 p.m., New York Live Arts, 219 West 19th Street, Chelsea, (212) 924-0077, newyorklivearts.org; $40, $32 for students and 65+. (Roslyn Sulcas)

★ Trisha Brown Dance Company (Friday and Saturday) The Trisha Brown Dance Company’s announcement that its appearance at the Brooklyn Academy of Music would feature what will be the final works of Ms. Brown’s career did not come as a great surprise to a dance world already aware of her health problems. The company will most likely go on performing Ms. Brown’s important body of work. But there is something poignant about these first performances in New York of the last works. “I’m going to toss my arms — if you catch them they’re yours” (2011) is a collaboration with the composer Alvin Curran (who will perform live) and the artist Burt Barr, who is Ms. Brown’s husband. The other new work, “Les Yeux et l’âme,” is a suite of dances from Ms. Brown’s production of the Rameau opera “Pygmalion,” first performed in Amsterdam in 2010. Also on the two programs is a solo, “Homemade,” danced by Vicky Shick, one of Ms. Brown’s early company members, and two emblematic pieces: the 1987 “Newark,” which has sound and costumes by Donald Judd, and the 1983 “Set and Reset,” with its hypnotic Laurie Anderson score and wonderful Robert Rauschenberg costumes. Essential. At 7:30 p.m., Howard Gilman Opera House, Brooklyn Academy of Music, 30 Lafayette Avenue, at Ashland Place, Fort Greene, Brooklyn, (718) 636-4100, bam.org; $20 to $70. (Sulcas)

Buglisi Dance Theater (Tuesday through Thursday; through Feb. 10) Martha Graham’s dramatic influence runs heavily through the work of Jacqulyn Buglisi, who established this company with other alumni of the Martha Graham Dance Company. Some of those founding members return to perform in the troupe’s 20th anniversary season, which features four world premieres (one by the emerging choreographer Katarzyna Skarpetowska), six repertory works, and excerpts from “Arenal” by Spain’s esteemed Nacho Duato. Luminaries from the ballet world — Martine van Hamel and Charles Askegard — make guest appearances. Tuesday and Wednesday at 7:30 p.m., Thursday at 8 p.m., Joyce Theater, 175 Eighth Avenue, at 19th Street, Chelsea, (212) 242-0800, joyce.org; $10 to $39. (Siobhan Burke)

CoolNY Dance Festival (Friday through Sunday and Thursday; through Feb. 10) One of several eclectic dance festivals organized annually by the choreographer Young Soon Kim, CoolNY returns for its 10th year with 60 companies presented over two weeks. Ms. Kim clearly wants to provide opportunities for emerging choreographers, but it’s unclear what connects the artists on each of 10 programs. This is a decidedly mixed-bag affair. Friday and Thursday at 7 and 9 p.m., Saturday at 2, 7 and 9 p.m., Sunday at 4 and 6 p.m., John Ryan Theater, 25 Jay Street, Dumbo, Brooklyn, whitewavedance.com. (Burke)

★ Sean Curran Company (Saturday) Sean Curran, who was both an Irish step dancer and a notable performer with Bill T. Jones/Arnie Zane Dance Company, has many strings to his choreographic bow. His work is witty and accessible, yet there has always been something Chaplin-esque about Mr. Curran’s onstage persona, a hint of the vulnerable loner, that translates into an emotional sensitivity in his dances. For his company’s 15th anniversary season, Mr. Curran presents two recent pieces: “Fireweather,” set to a Charles Wuorinen score for two pianos, and “Left Exit,” which uses recorded voices, speaking from texts that offer competing ideas about secular reasoning and religious faith. At 2 and 8 p.m., Joyce Theater, 175 Eighth Avenue, at 19th Street, Chelsea, (212) 242-0800, joyce.org; $10 to $39. (Sulcas)

Dance on Camera Festival (Friday through Tuesday) Ice dancing, coming-of-age stories and the unlikely choreography of trash collection are just a few of the subjects explored in this year’s festival, presented by the Dance Films Association and the Film Society of Lincoln Center. The lineup of more than 60 films in this 41st edition runs the gamut from documentaries (like Marie-Hélène Rebois’s inside look at the closure of the Merce Cunningham Dance Company) to poetic, abstract shorts by Shirley Clarke, a pioneer of dance-for-the-camera. Opening night features the premiere of Alan Brown’s steamy drama — an indie “Center Stage”? — about a small contemporary dance company in the big city. At various times, Elinor Bunin Munroe Film Center, Lincoln Center, 144 West 65th Street, (212) 875-5600, filmlinc.com; $13. (Burke)

★ Douglas Dunn (Thursday through Feb. 9) Mr. Dunn’s “Cassations,” glowingly received at its December premiere at the 92nd Street Y, is already returning. Danspace Project remounts the beguiling suite of dances, set to operatic arias and structured around the coming together and pulling apart of groups of men and women. It may sound simple, but Mr. Dunn has a way of mining layers of complexity from the most basic foundation. At 8 p.m., Danspace Project, St. Mark’s Church, 131 East 10th Street, East Village, (866) 811-4111, danspaceproject.org; $18. (Burke)

★ FLICfest 2013 (Friday and Saturday) Founded three years ago by Jeramy Zimmerman, FLICfest gives choreographers a chance to attempt full-length pieces rather than the shorter ones that festivals usually require. Fourteen choreographers (some of them in tandem) will participate over two weekends, starting with Jillian Sweeney and Summation Dance Company on Thursday. Cabaret performances follow at 10:30 each night; what’s not to like? At 7:30 and 9 p.m., Irondale Center, 85 South Oxford Street, Fort Greene, Brooklyn, (866) 811-4111, irondale.org; $25 (includes both shows and cabaret), $20 for artists and students. (Sulcas)

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Fridays at Noon (Friday) The next edition of this free series takes us back to the 1930s and the politically charged works of the New Dance Group. Founded in 1932, the collective of choreographers believed in movement as a vehicle for social activism. This program includes pieces by some of its most distinguished members, including Donald McKayle, Anna Sokolow and Pearl Primus, in addition to a panel discussion with the historian Victoria Phillips Geduld and others. At noon, 92nd Street Y, 1395 Lexington Avenue, (212) 415-5500, 92y.org; free. (Burke)

★ Harrison Atelier with Silas Riener (Thursday through Feb. 9) The design collective Harrison Atelier, directed by a Yale architecture professor (Ariane Harrison) and a designer and biotechnologist (Seth Harrison), presents its second collaboration with the choreographer Silas Riener. If “VEAL” is anything like their 2011 “Pharmacophore: Architectural Placebo,” it will plunge its audience into a futuristic landscape where human bodies and synthetic materials form an eerie symbiosis. Five installations (including a performance choreographed by Mr. Riener) spring up around modern theories and ancient myths about the slaughtering of animals and the displacement of nature by technology. At 7:30 p.m., Invisible Dog Art Center, 51 Bergen Street, Cobble Hill, Brooklyn, (347) 560-3641, theinvisibledog.org, reservation requests can be e-mailed to simon@theinvisibledog.org; $10 suggested donation. (Burke)

★ New York City Ballet (Friday through Sunday, Tuesday through Thursday; through Feb. 24) Justin Peck, the company’s fast-rising choreographic star (also a member of the corps de ballet), is in good company this week, sharing bills with Balanchine, Robbins and Alexei Ratmansky. On Saturday and Sunday afternoons his effervescent “Year of the Rabbit” is sandwiched between Robbins’s arresting, Philip Glass-fueled “Glass Pieces” and Balanchine’s regal “Vienna Waltzes.” New this season, his “Paz de La Jolla” returns on Saturday and Wednesday nights. His work is not part of Friday’s specially priced program ($29 for every seat in the house), though there will be plenty to admire in this evening of Christopher Wheeldon, William Forsythe, Peter Martins and Balanchine. Friday at 8 p.m., Saturday at 2 and 8 p.m., Sunday at 3 p.m., Tuesday through Thursday at 7:30 p.m., David H. Koch Theater, Lincoln Center, (212) 496-0600, nycballet.com; $29 to $155. (Burke)

SPLICE: Neal Beasley and Bradley Teal Ellis (Wednesday and Thursday; through Feb. 9) The choreographers in this series generally split the bill neatly in two. But Mr. Beasley, a dancer with Trisha Brown, and Mr. Ellis, a seasoned practitioner of contact improvisation, are taking a fresh approach to the shared-evening format, interweaving vignettes of their work and allowing viewers to wander throughout the space. Mr. Beasley’s “every adam belonging to me” and Mr. Ellis’s “(American)Guilt” seem like a natural pairing (at least on paper), both questioning traditional representations of gender and American identity. At 7:30 p.m., Dance New Amsterdam, 280 Broadway, at Chambers Street, Lower Manhattan, (212) 625-8369, dnadance.org; $12 in advance, $17 day of performance, $14 for students and 65+. (Burke)

State Ballet Theater of Russia (Friday) Known for sticking to the classics, this company returns to Newark with its full-length “Cinderella,” choreographed by Vladimir Vasiliev to Prokofiev’s score. At 7:30 p.m., New Jersey Performing Arts Center, 1 Center Street, Newark, (888) 466-5722, njpac.org; $20 to $80. (Burke)

Meryl Tankard (Thursday through Feb. 9) In honor of the centennial of “The Rite of Spring,” Ms. Tankard, one of Australia’s best-known contemporary dance makers, offers the New York premiere of her take on that 1913 ballet, “The Oracle.” The explosive solo spotlights the virtuosic Australian dancer Paul White, who will soon follow in Ms. Tankard’s footsteps when he joins Tanztheater Wuppertal (the company founded by Pina Bausch), where Ms. Tankard danced for 10 years. At 8 p.m., N.Y.U. Skirball Center for the Performing Arts, 566 La Guardia Place, at Washington Square South, Greenwich Village, (212) 352-3101, nyuskirball.org; $30 to $49. (Burke)

Working Women (Friday and Sunday) A spinoff from a one-night concert last summer, this program, presented by Gotham Arts Exchange, shows work by seven women. It’s a fine lineup, with most, but not all, of the names familiar to dancegoers. Whether or not you know the work of Camille A. Brown, Monica Bill Barnes, Kate Weare, Janis Brenner, Jane Comfort or Loni Landon, the variety of styles and aesthetics here suggests a good deal to enjoy. Friday at 8 p.m., Sunday at 2 and 7:30 p.m., Joyce Theater, 175 Eighth Avenue, at 19th Street, Chelsea, (212) 242-0800, joyce.org; $10 to $39. (Sulcas)

Correction: February 2, 2013

A dance entry in the Listings pages on Friday about a collaboration between the Harrison Atelier design collective and the choreographer Silas Riener, at Invisible Dog Art Center in Brooklyn, misstated the given name of a leader of the collective. She is Ariane Harrison, not Anne.